{
  "id": "2410.06092",
  "version": "v1",
  "published": "2024-10-08T14:48:12.000Z",
  "updated": "2024-10-08T14:48:12.000Z",
  "title": "Restriction of Fractional Derivatives of the Fourier Transform",
  "authors": [
    "Michael Goldberg",
    "Chun Ho Lau"
  ],
  "categories": [
    "math.FA",
    "math.CA"
  ],
  "abstract": "In this paper, we showed that for suitable $(\\beta,p, s,\\ell)$ the $\\beta$-order fractional derivative with respect to the last coordinate of the Fourier transform of an $L^p(\\mathbb{R}^n)$ function is in $H^{-s}$ after restricting to a graph of a function with non-vanishing Gaussian curvature provided that the restriction of the Fourier transform of such function to the surface is in $H^{\\ell}$. This is a generalization of the result in \\cite{GoldStol}*{Theorem 1.12}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-08T14:48:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42B10",
      "42B20"
    ],
    "keywords": [
      "fourier transform",
      "restriction",
      "non-vanishing gaussian curvature",
      "coordinate",
      "order fractional derivative"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}